How to call python animation node operator?
For Animation Nodes I developed a system that automatically generates operators for certain functions on nodes. Otherwise I would have to write a lot of overhead code all the time. This is why the operator has a weird name like invoke_function_1. It also explains why the operator does not exist when you run your script at first. The operators are only created when needed.

Those operators are only should only used on the UI. In all other cases you should call the underlying functions directly. 

In your case you have to do something like this: bpy.data.node_groups["NodeTree"].nodes["summary_list"].newInputSocket().